This well-known standard work is an expansion by O. G. Tietjens of a famous series of lectures delivered by Professor Prandtl at the Kaiser Wilhelm Institute for Flow Research. Based on Prandtl's own work, it combines a considerable amount of original material with unique insights and presentations. Wherever possible, the hydrodynamic theory presented is tied to practical experience, while experimental results are in turn related back to the underlying theory and the fundamental physical laws. Partial contents: the statics of liquids and gases (equilibrium and stability, application of the pressure equation, static-lift on gas-filled aircraft, surface tension); kinematics of liquids and gases (geometry of the vector field, acceleration of a fluid particle, equation of continuity); the dynamics of non-viscous fluids (the Eulerian equation, potential motion, two-dimensional potential motion, vortex motion, the influence of compressibility, the equation of Navier-Stokes for viscous fluids). While the presentation is fundamentally physical rather than mathematical, when proofs are given they are rigorous and vector analysis is employed. But the text is remarkably clear and understandable, ideally suited for both research workers and graduate-level students.